Answer:
Based on the given information, the relationship between List X and List Y is that List Y is formed by adding 2 to each number in List X. Let's analyze each option to determine which one must be equal for the two lists:
- The mean: Adding 2 to each number in List X would shift the values up by 2 units, but this would not affect the mean. Both lists would have the same mean value as the original list, so the mean does not have to be equal.
- The median: Since the same amount (2) is added to each number in List X, the order of the numbers remains unchanged. Thus, the median value in List Y would also be shifted up by 2 units compared to List X. However, it is not guaranteed that the median values of List X and List Y will be equal.
- The maximum: Adding 2 to every number in List X would simply increase the largest number by 2, resulting in a different maximum value for List Y compared to List X. Therefore, the maximum does not have to be equal.
- The range: The range is the absolute difference between the maximum and minimum values in a list. Since the maximum value would be different for List X and List Y (as discussed earlier), the ranges of the two lists would also be different. Therefore, the range does not have to be equal.
Based on the analysis, none of the options (mean, median, maximum, range) must be equal between List X and List Y.